Transcript Uncertainty and Sig Figs - OG

Uncertainty and Sig Figs
Notes on how to do sig figs,
rounding, and calculations
Accuracy depends on…
• Error or uncertainty always exists in
any measurement.
• skill of the measurer
• conditions of measurement
• measuring instruments
Significant Figures
A. DEF:
1. Number of all known digits reported
in measurements plus one estimated
digit
2. The term significant does not mean
certain
Rules for Counting Sig Figs
I.) Nonzero Integers (1 – 9)
- nonzero numbers ALWAYS count
as sig figs
-Ex: 5281 has 4 sig figs
• How many sig figs are in…
927,813,451
Answer: 9 sig figs!
Sig Fig Rules
II.) Zero’s (3 types of “zero” rules)
1.) Leading Zeros:
• Zeros that comes before nonzero
digits are NEVER counted as sig figs
- Ex: 0.0039 has 2 sig figs
How many sig figs in this number:
0.00000000000099855
Answer: 5 sig figs
2.) Captive Zero:
• Zeros that fall between nonzero
digits ALWAYS count as sig figs
- Ex: 1.2008 has 5 sig figs
How many sig figs in this number:
6.00800100514
Answer: 12 sig figs
3.) Trailing Zeros
• Zeros at the end of a number
ALWAYS count as significant figures
- Ex: 500 has 3 sig figs
How many sig figs in the number:
13,000
Answer: 5 sig figs
3) Exact Numbers
• Numbers that are not obtained with
measuring devices
- determined by COUNTING
- Ex: 4 dogs, 18 chickens
- These numbers are assumed to have
UNLIMITED number of sig figs
Practice – write down your answers
How many sig figs are in each of the
following?
1)
2)
3)
4)
5)
6)
6.0006 ___________
3869 ___________
23 puppies ____________
600 __________
1.030 _____________
0.010080 ____________
Practice Answers
1)
2)
3)
4)
5)
6)
5
4
Unlimited
3
4
5
Rules for Rounding
•
Use only the 1st number to the right
of the last sig fig you want in your
number
1) Less than 5 – round down (drop off)
Ex: 1.432 rounded to 3 sig figs is
_____ 1.43
2) Greater than 5 – round up
Ex: 3.486 rounded to 3 sig figs is
_____ 3.49
Sig Figs in Calculations
• Multiplication and Division
– The number of sig figs in your answer
should be the same as the measurement
with the smallest number of sig figs
– Ex: 2.5 x 2.00 = _______
– How many sig figs can we have? _2___
– Answer is _5.0______
Practice some x & ÷
1)
2)
3)
4)
•
23.5x104 x 1.8x104 =
456/32 =
25/5.0 =
10/4 =
Answers:
–
–
–
–
1) 4230000000 = 4200000000 or
4.2x109
2) 14.25 = 14
3) 5 = 5.0
4) 2.5 = 2
1)
2)
3)
4)
5)
6)
•
Practice with + & -
56 + 296.5 =
.45 – 0.003 =
30 + 156.70 =
6.8x105 – 5.001x103 =
7.1x1010 – 1.11x109 =
3.56x104 + 4.1x102 =
Answers:
1)
2)
3)
4)
5)
6)
352.5 = 352
0.447 = 0.45
186.7 = 190
674999 = 670000 or 6.7x105
6.989x1010 = 7.0x1010
36010 = 36000 or 3.60x104